Samples returned from Mars would be placed under quarantine at a Sample Receiving Facility (SRF) until they are considered safe to release to other laboratories for further study. The process of determining whether samples are safe for release, which may involve detailed analysis and/or sterilization, is expected to take several months. However, the process of breaking the sample tube seal and extracting the headspace gas will perturb local equilibrium conditions between gas and rock and set in motion irreversible processes that proceed as a function of time. Unless these time-sensitive processes are understood, planned for, and/or monitored during the quarantine period, scientific information expected from further analysis may be lost forever. At least four processes underpin the time-sensitivity of Mars returned sample science: (1) degradation of organic material of potential biological origin, (2) modification of sample headspace gas composition, (3) mineral-volatile exchange, and (4) oxidation/reduction of redox-sensitive materials. Available constraints on the timescales associated with these processes supports the conclusion that an SRF must have the capability to characterize attributes such as sample tube headspace gas composition, organic material of potential biological origin, as well as volatiles and their solid-phase hosts. Because most time-sensitive investigations are also sensitive to sterilization, these must be completed inside the SRF and on timescales of several months or less. To that end, we detail recommendations for how sample preparation and analysis could complete these investigations as efficiently as possible within an SRF. Finally, because constraints on characteristic timescales that define time-sensitivity for some processes are uncertain, future work should focus on: (1) quantifying the timescales of volatile exchange for core material physically and mineralogically similar to samples expected to be returned from Mars, and (2) identifying and developing stabilization or temporary storage strategies that mitigate volatile exchange until analysis can be completed.